Contents: Reptation Quantum Monte Carlo; Phase separation in the 2D Hubbard model; Calculations of exchange frequencies with path integral Monte Carlo; Monte Carlo Methods in Nuclear Physics; Path-int . . . . .

These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are fir . . . . .

Contents: Hartree-Fock theory, Exact Diagonalization, Lanczos Alghorithm, Langevin dynamics, Stochastic minimization, Variational Monte Carlo, Green Function Monte Carlo.

This article first gives a concise introduction to quantum phase transitions, emphasizing similarities with and differences to classical thermal transitions. After pointing out the computational chall . . . . .

Contents:introduction; quantum monte carlo methods; nodal properties of fermionic wave functions; Pfaffian pairing wave functions; Backflow correlations in slater and pfaffian wave functions; example . . . . .

A review of the Loop Algorithm, its generalizations, and its relation to some other Monte Carlo techniques is given. The loop algorithm is a Quantum Monte Carlo procedure which employs nonlocal change . . . . .

This is a book chapter soon to appear (2002) in the "Handbook for Numerical Analysis" volume dedicated to "Computational Chemistry" edited by Claude Le Bris. The series editors are P.G. Ciarlet and J. . . . . .

Contents: Monte Carlo Integration; Classical Monte Carlo Simulations; Cluster Algorithms; The Wang-Landau Algorithm; Quantum Monte Carlo Algorithms; Stochastic Series Expansion; The Wang-Landau Algo . . . . .

This article describes the variational and fixed-node diffusion quantum Monte Carlo methods and how they may be used to calculate the properties of many-electron systems.

In these lectures, I will briefly review some of the Quantum Monte Carlo (QMC) methods that have been used to calculate properties of the electron gas and review properties that have been computed w . . . . .

Contents: Introduction; Monte Carlo integration; Classical Monte Carlo simulations; The quantum Monte Carlo loop algorithm; Exact diagonalization.

Abstract: The quantum Monte Carlo methods represent a powerful and broadly applicable computational tool for finding very accurate solutions of the stationary Schroedinger equation for atoms, mole . . . . .

Variational wave functions containing electronic pairing and suppressed charge fluctuations (i.e., projected BCS states) have been proposed as the paradigm for disordered magnetic systems (including s . . . . .

This article gives an introduction to the multilevel blocking (MLB) approach to both the fermion and the dynamical sign problem in path-integral Monte Carlo simulations. MLB is able to substantially r . . . . .

They present a new technics used to develop a new quantum simulation method which allows to calculate the ground-state expectation values of local observables without any mixed estimates.

Review about fermion nodes problems.

This article discusses the basic properties of the path integral method for continuum fermions, focusing on the restricted path integral (RPIMC) approach.

They review random walks and the quantum Monte Carlo methods used to simulate the ground state of many-body quantum systems, namely variational Monte Carlo and projector Monte Carlo.

They tutorially review the determinantal Quantum Monte Carlo method for fermionic systems, using the Hubbard model as a case study. Starting with the basic ingredients of Monte Carlo simulations for c . . . . .

A self-contained and tutorial presentation of the diffusion Monte Carlo method for determining the ground state energy and wave function of quantum systems is provided. First, the theoretical basis of . . . . .

Contents: Basics, quantum Monte Carlo and statistical mechanics; Stochastic diagonalization; Quantum Monte Carlo for lattice bosons; Variational Monte Carlo in solids; Response functions from quantum . . . . .